The future chapter of the series, BioShock 4, could be a PlayStation exclusive (perhaps timed-exclusive). These are the words of a well-known leaker.
Bioshock 4 to be a PlayStation 5 exclusive game
In 2019, 2K Games announced that they are working on a new Bioshock 4 and that it will be in development for several more years. So it will take a while before the game comes out, but the publisher will be present at E3, so we may hear more soon.
This would be the first time that information will be really shared, because we know next to nothing about the game. Interestingly, however, there is a new rumor shared by YouTuber XboxEra, who states in its new video that the upcoming BioShock will be exclusive to the PS5.
That is all the insider knows, so if this is correct, the question still remains whether it is temporary or permanently exclusive to the PlayStation console. Xbox Era is not aware of that.
A temporary exclusivity seems the most obvious, given that the previous adventures of the game have released on all platforms like PC, Xbox One. In addition, Sony more often closes such deals, like for example the upcoming Deathloop.
Recall that the first BioShock was exclusive to Xbox 360 and PC for just over a year. While this leaker has a history of hits behind it, for now we’d better take this information with a grain of salt until the proper official announcements are made.